ON THE EQUIVALENCE OF RAMANUJANS PARTITION-IDENTITIES AND A CONNECTION WITH THE ROGERS-RAMANUJAN CONTINUED-FRACTION

A famous identity of Ramanujan connected with partitions module 5 is s hown to be equivalent to another identity of Ramanujan. The latter ide ntity is used to establish a differential equation for the Rogers-Rama nujan continued fraction found in Ramanujan's lost notebook. We also p rove that two other identities of Ramanujan are equivalent, one of whi ch is associated with Ramanujan's partition congruence module 7. Last, we give a new proof of the transformation formula for the Dedekind et a-function, which is used in our proofs of equivalence. (C) 1996 Acade mic Press, Inc.